by Erin Gottschalk, Simon Johnson, Meghan, Elizabeth Nguyen, and Brooke Rogers*.

*Brooke helped the group work through the problem set but was unfortunately unable to attend camp during the blog writing.

What We Did:

Knot theory has many different applications in math including algebra and geometry, and (outside of math) physics. We learned that we can use algebraic techniques to describe knots. When trying to understand knot theory we learned that it is very helpful to work in a group and read the definitions out loud. Us working together was key in understanding knot theory.

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by Nya Batson, Monique Dacanay, Emily Gao, and Staci Tranquille.

Hello! And welcome to the realm of quantum mechanics!  First off, what in the world is quantum mechanics? Let’s start with a brief introduction.

What is Quantum Mechanics?

Quantum mechanics is one of the most important branches of physics. It focuses on the laws of nature at three different levels: molecular, atomic, and subatomic. Quantum mechanics has a variety of important concepts; the following are some that we learned through our problem set: Planck’s law, the photoelectric effect, and wave-particle duality.  A crucial element of quantum mechanics is understanding that everything has characteristics of both waves and particles. We will touch on this and many other topics later on.

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by Alysia Davis, Alyssa Drumgold, Pascale Gomez, Delaney Washington, and Auden Wolfe.

 

Intro to Number Systems

As children we grew up counting in the base ten system (1, 2, 3, etc). However, base ten is only one of many numerical systems. Over these past to weeks at Girls Talk Math at UNC, our  task was to explore other number systems that are not as frequently used as the base 10 system, specifically binary and hexadecimal number systems.

 

Binary

The exact definition of binary is related to using a system of numerical notation that has 2 rather than 10 as a base. This means only two single digits are used, 0 and 1. 

Binary is used for data storage. Binary basically makes it easier for computer processors to understand and interpret incoming information/instructions.

Binary was first discussed by Gottfried Leibniz in 1689 but binary numerical systems were not put to use until a binary converter was created hundreds of years later. The binary system was officially implemented just before the beginning of the nineteenth century.

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by Camille Clark, Layke Jones, Aekta Kallepalli, Maya Mukerjee, and Caroline Zhou.

 

Euler Characteristics

Euler characteristics are defined by the equation V- E + F = 2 where V = number of vertices, E = number of edges or nodes, and F = number of faces. Sometimes though, the equation V – E + F = 2 does not work for all situations because the solution can give various outcomes due to the dimensions and simplicity of the object. If 2 objects are topologically the same, they will have the same Euler characteristics. For all simple polygons, the Euler characteristics equal one. Figures with holes don’t follow these conventions as the holes in these figures add additional faces and edges not proportional to the formulas for simple figures.

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by Kayla Aguilar, Maris James, and Aynsley S.

Data is all around us, but it has to be studied in some way, right? How else are we supposed to know what it’s about? That’s what graph theory and network science are for! To organize and connect data mathematicians use networks and graphs as well as scientific computing (like coding).

Network science is an application-based study of graphs. To understand network science, we first have to understand the graphs:

Graph Theory

Graphs represent data through nodes, which are the separate points of a graph, and edges, which connect the nodes. There are two types of graphs: directed and undirected graphs. Directed graphs rely on the order of the vertices to be the same, while undirected graphs don’t rely on the order of the nodes.

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